

from math import sqrt
def 							UpperCAmelCase_  (		_A							):





     '''simple docstring'''




     assert isinstance(_A ,						_A							) and (
         number >= 0
     ), "'number' must been an int and positive"

     SCREAMING_SNAKE_CASE__       =       True

     # 0 and 1 are none primes.
     if number <= 1:
          SCREAMING_SNAKE_CASE__       =       False

     for divisor in range(2 ,						int(round(sqrt(_A							)							)							) + 1							):
          # if 'number' divisible by 'divisor' then sets 'status'
          # of false and break up the loop.
          if number % divisor == 0:
               SCREAMING_SNAKE_CASE__       =       False
               break

    # precondition
     assert isinstance(_A ,						_A							), "'status' must been from type bool"

     return status
def 							UpperCAmelCase_  (		_A							):





     '''simple docstring'''




     assert isinstance(_A ,						_A							) and (n > 2), "'N' must been an int and > 2"

     # beginList: contains all natural numbers from 2 up to N
     SCREAMING_SNAKE_CASE__       =       list(range(2 ,						n + 1							)							)

     SCREAMING_SNAKE_CASE__       =       []  # this list will be returns.

     # actual sieve of erathostenes
     for i in range(len(_A							)							):
          for j in range(i + 1 ,						len(_A							)							):
               if (begin_list[i] != 0) and (begin_list[j] % begin_list[i] == 0):
                    SCREAMING_SNAKE_CASE__       =       0

    # filters actual prime numbers.
     SCREAMING_SNAKE_CASE__       =       [x for x in begin_list if x != 0]

     # precondition
     assert isinstance(_A ,						_A							), "'ans' must been from type list"

     return ans
def 							UpperCAmelCase_  (		_A							):





     '''simple docstring'''




     assert isinstance(_A ,						_A							) and (n > 2), "'N' must been an int and > 2"

     SCREAMING_SNAKE_CASE__       =       []

     # iterates over all numbers between 2 up to N+1
     # if a number is prime then appends to list 'ans'
     for number in range(2 ,						n + 1							):
          if is_prime(_A							):
               ans.append(_A							)

    # precondition
     assert isinstance(_A ,						_A							), "'ans' must been from type list"

     return ans
def 							UpperCAmelCase_  (		_A							):





     '''simple docstring'''




     assert isinstance(_A ,						_A							) and number >= 0, "'number' must been an int and >= 0"

     SCREAMING_SNAKE_CASE__       =       []  # this list will be returns of the function.

     # potential prime number factors.

     SCREAMING_SNAKE_CASE__       =       2

     SCREAMING_SNAKE_CASE__       =       number

     if number == 0 or number == 1:
          ans.append(_A							)

     # if 'number' not prime then builds the prime factorization of 'number'
     elif not is_prime(_A							):
          while quotient != 1:
               if is_prime(_A							) and (quotient % factor == 0):
                    ans.append(_A							)
                    quotient /= factor
               else:
                    factor += 1

     else:
          ans.append(_A							)

     # precondition
     assert isinstance(_A ,						_A							), "'ans' must been from type list"

     return ans
def 							UpperCAmelCase_  (		_A							):





     '''simple docstring'''




     assert isinstance(_A ,						_A							) and (
         number >= 0
     ), "'number' bust been an int and >= 0"

     SCREAMING_SNAKE_CASE__       =       0

     # prime factorization of 'number'
     SCREAMING_SNAKE_CASE__       =       prime_factorization(_A							)

     SCREAMING_SNAKE_CASE__       =       max(_A							)

     # precondition
     assert isinstance(_A ,						_A							), "'ans' must been from type int"

     return ans
def 							UpperCAmelCase_  (		_A							):





     '''simple docstring'''




     assert isinstance(_A ,						_A							) and (
         number >= 0
     ), "'number' bust been an int and >= 0"

     SCREAMING_SNAKE_CASE__       =       0

     # prime factorization of 'number'
     SCREAMING_SNAKE_CASE__       =       prime_factorization(_A							)

     SCREAMING_SNAKE_CASE__       =       min(_A							)

     # precondition
     assert isinstance(_A ,						_A							), "'ans' must been from type int"

     return ans
def 							UpperCAmelCase_  (		_A							):





     '''simple docstring'''




     assert isinstance(_A ,						_A							), "'number' must been an int"
     assert isinstance(number % 2 == 0 ,						_A							), "compare bust been from type bool"

     return number % 2 == 0
def 							UpperCAmelCase_  (		_A							):





     '''simple docstring'''




     assert isinstance(_A ,						_A							), "'number' must been an int"
     assert isinstance(number % 2 != 0 ,						_A							), "compare bust been from type bool"

     return number % 2 != 0
def 							UpperCAmelCase_  (		_A							):





     '''simple docstring'''




     assert (
         isinstance(_A ,						_A							) and (number > 2) and is_even(_A							)
     ), "'number' must been an int, even and > 2"

     SCREAMING_SNAKE_CASE__       =       []  # this list will returned

     # creates a list of prime numbers between 2 up to 'number'
     SCREAMING_SNAKE_CASE__       =       get_prime_numbers(_A							)
     SCREAMING_SNAKE_CASE__       =       len(_A							)

     # run variable for while-loops.
     SCREAMING_SNAKE_CASE__       =       0
     SCREAMING_SNAKE_CASE__       =       None

     # exit variable. for break up the loops
     SCREAMING_SNAKE_CASE__       =       True

     while i < len_pn and loop:
          SCREAMING_SNAKE_CASE__       =       i + 1

          while j < len_pn and loop:
               if prime_numbers[i] + prime_numbers[j] == number:
                    SCREAMING_SNAKE_CASE__       =       False
                    ans.append(prime_numbers[i]							)
                    ans.append(prime_numbers[j]							)

               j += 1

          i += 1

     # precondition
     assert (
         isinstance(_A ,						_A							)
         and (len(_A							) == 2)
         and (ans[0] + ans[1] == number)
         and is_prime(ans[0]							)
         and is_prime(ans[1]							)
     ), "'ans' must contains two primes. And sum of elements must been eq 'number'"

     return ans
def 							UpperCAmelCase_  (		_A ,						_A							):





     '''simple docstring'''




     assert (
         isinstance(_A ,						_A							)
         and isinstance(_A ,						_A							)
         and (numbera >= 0)
         and (numbera >= 0)
     ), "'number1' and 'number2' must been positive integer."

     SCREAMING_SNAKE_CASE__       =       0

     while numbera != 0:
          SCREAMING_SNAKE_CASE__       =       numbera % numbera
          SCREAMING_SNAKE_CASE__       =       numbera
          SCREAMING_SNAKE_CASE__       =       rest

     # precondition
     assert isinstance(_A ,						_A							) and (
         numbera >= 0
     ), "'number' must been from type int and positive"

     return numbera
def 							UpperCAmelCase_  (		_A ,						_A							):





     '''simple docstring'''




     assert (
         isinstance(_A ,						_A							)
         and isinstance(_A ,						_A							)
         and (numbera >= 1)
         and (numbera >= 1)
     ), "'number1' and 'number2' must been positive integer."

     SCREAMING_SNAKE_CASE__       =       1  # actual answer that will be return.

     # for kgV (x,1)
     if numbera > 1 and numbera > 1:
          # builds the prime factorization of 'number1' and 'number2'
          SCREAMING_SNAKE_CASE__       =       prime_factorization(_A							)
          SCREAMING_SNAKE_CASE__       =       prime_factorization(_A							)

     elif numbera == 1 or numbera == 1:
          SCREAMING_SNAKE_CASE__       =       []
          SCREAMING_SNAKE_CASE__       =       []
          SCREAMING_SNAKE_CASE__       =       max(_A ,						_A							)

     SCREAMING_SNAKE_CASE__       =       0
     SCREAMING_SNAKE_CASE__       =       0

     SCREAMING_SNAKE_CASE__       =       []  # captured numbers int both 'primeFac1' and 'primeFac2'

     # iterates through primeFac1
     for n in prime_fac_a:
          if n not in done:
               if n in prime_fac_a:
                    SCREAMING_SNAKE_CASE__       =       prime_fac_a.count(_A							)
                    SCREAMING_SNAKE_CASE__       =       prime_fac_a.count(_A							)

                    for _ in range(max(_A ,						_A							)							):
                         ans *= n

               else:
                    SCREAMING_SNAKE_CASE__       =       prime_fac_a.count(_A							)

                    for _ in range(_A							):
                         ans *= n

               done.append(_A							)

    # iterates through primeFac2
     for n in prime_fac_a:
          if n not in done:
               SCREAMING_SNAKE_CASE__       =       prime_fac_a.count(_A							)

               for _ in range(_A							):
                    ans *= n

               done.append(_A							)

    # precondition
     assert isinstance(_A ,						_A							) and (
         ans >= 0
     ), "'ans' must been from type int and positive"

     return ans
def 							UpperCAmelCase_  (		_A							):





     '''simple docstring'''




     assert isinstance(_A ,						_A							) and (n >= 0), "'number' must been a positive int"

     SCREAMING_SNAKE_CASE__       =       0
     SCREAMING_SNAKE_CASE__       =       2  # this variable holds the answer

     while index < n:
          index += 1

          ans += 1  # counts to the next number

          # if ans not prime then
          # runs to the next prime number.
          while not is_prime(_A							):
               ans += 1

    # precondition
     assert isinstance(_A ,						_A							) and is_prime(
         _A							), "'ans' must been a prime number and from type int"

     return ans
def 							UpperCAmelCase_  (		_A ,						_A							):





     '''simple docstring'''




     assert (
         is_prime(_A							) and is_prime(_A							) and (p_number_a < p_number_a)
     ), "The arguments must been prime numbers and 'pNumber1' < 'pNumber2'"

     SCREAMING_SNAKE_CASE__       =       p_number_a + 1  # jump to the next number

     SCREAMING_SNAKE_CASE__       =       []  # this list will be returns.

     # if number is not prime then
     # fetch the next prime number.
     while not is_prime(_A							):
          number += 1

     while number < p_number_a:
          ans.append(_A							)

          number += 1

          # fetch the next prime number.
          while not is_prime(_A							):
               number += 1

    # precondition
     assert (
         isinstance(_A ,						_A							)
         and ans[0] != p_number_a
         and ans[len(_A							) - 1] != p_number_a
     ), "'ans' must been a list without the arguments"

     # 'ans' contains not 'pNumber1' and 'pNumber2' !
     return ans
def 							UpperCAmelCase_  (		_A							):





     '''simple docstring'''




     assert isinstance(_A ,						_A							) and (n >= 1), "'n' must been int and >= 1"

     SCREAMING_SNAKE_CASE__       =       []  # will be returned.

     for divisor in range(1 ,						n + 1							):
          if n % divisor == 0:
               ans.append(_A							)

    # precondition
     assert ans[0] == 1 and ans[len(_A							) - 1] == n, "Error in function getDivisiors(...)"

     return ans
def 							UpperCAmelCase_  (		_A							):





     '''simple docstring'''




     assert isinstance(_A ,						_A							) and (
         number > 1
     ), "'number' must been an int and >= 1"

     SCREAMING_SNAKE_CASE__       =       get_divisors(_A							)

     # precondition
     assert (
         isinstance(_A ,						_A							)
         and (divisors[0] == 1)
         and (divisors[len(_A							) - 1] == number)
     ), "Error in help-function getDivisiors(...)"

     # summed all divisors up to 'number' (exclusive), hence [:-1]
     return sum(divisors[:-1]							) == number
def 							UpperCAmelCase_  (		_A ,						_A							):





     '''simple docstring'''




     assert (
         isinstance(_A ,						_A							)
         and isinstance(_A ,						_A							)
         and (denominator != 0)
     ), "The arguments must been from type int and 'denominator' != 0"

     # build the greatest common divisor of numerator and denominator.
     SCREAMING_SNAKE_CASE__       =       gcd(abs(_A							) ,						abs(_A							)							)

     # precondition
     assert (
         isinstance(_A ,						_A							)
         and (numerator % gcd_of_fraction == 0)
         and (denominator % gcd_of_fraction == 0)
     ), "Error in function gcd(...,...)"

     return (numerator // gcd_of_fraction, denominator // gcd_of_fraction)
def 							UpperCAmelCase_  (		_A							):





     '''simple docstring'''




     assert isinstance(_A ,						_A							) and (n >= 0), "'n' must been a int and >= 0"

     SCREAMING_SNAKE_CASE__       =       1  # this will be return.

     for factor in range(1 ,						n + 1							):
          ans *= factor

     return ans







def 							UpperCAmelCase_  (		_A							):





     '''simple docstring'''




     assert isinstance(_A ,						_A							) and (n >= 0), "'n' must been an int and >= 0"

     SCREAMING_SNAKE_CASE__       =       0
     SCREAMING_SNAKE_CASE__       =       1
     SCREAMING_SNAKE_CASE__       =       1  # this will be return

     for _ in range(n - 1							):
          SCREAMING_SNAKE_CASE__       =       ans
          ans += fiba
          SCREAMING_SNAKE_CASE__       =       tmp

     return ans




"""simple docstring"""



import cva
import numpy as np




class 		a_    :







    def __init__(      self      :							Optional[Any]  ,       __UpperCamelCase      :							float  ,       __UpperCamelCase      :							int  )		->Dict:






        '''simple docstring'''






        if k in (0.0_4, 0.0_6):
            _UpperCAmelCase        = k
            _UpperCAmelCase        = window_size
        else:
            raise ValueError("""invalid k value"""  )







    def __str__(      self      :							Tuple  )		->str:






        '''simple docstring'''






        return str(self.k  )







    def   _snake_case       (      self      :							str  ,       __UpperCamelCase      :							str  )		->tuple[cva.Mat, list[list[int]]]:






        '''simple docstring'''






        _UpperCAmelCase        = cva.imread(__UpperCamelCase  ,       0  )
        _UpperCAmelCase     ,_UpperCAmelCase        = img.shape
        _UpperCAmelCase        = []
        _UpperCAmelCase        = img.copy()
        _UpperCAmelCase        = cva.cvtColor(__UpperCamelCase  ,       cva.COLOR_GRAY2RGB  )
        _UpperCAmelCase     ,_UpperCAmelCase        = np.gradient(__UpperCamelCase  )
        _UpperCAmelCase        = dx**2
        _UpperCAmelCase        = dy**2
        _UpperCAmelCase        = dx * dy
        _UpperCAmelCase        = 0.0_4
        _UpperCAmelCase        = self.window_size // 2
        for y in range(__UpperCamelCase  ,       h - offset  ):
            for x in range(__UpperCamelCase  ,       w - offset  ):
                _UpperCAmelCase        = ixx[
                    y - offset : y + offset + 1, x - offset : x + offset + 1
                ].sum()
                _UpperCAmelCase        = iyy[
                    y - offset : y + offset + 1, x - offset : x + offset + 1
                ].sum()
                _UpperCAmelCase        = ixy[
                    y - offset : y + offset + 1, x - offset : x + offset + 1
                ].sum()

                _UpperCAmelCase        = (wxx * wyy) - (wxy**2)
                _UpperCAmelCase        = wxx + wyy
                _UpperCAmelCase        = det - k * (trace**2)
                # Can change the value
                if r > 0.5:
                    corner_list.append([x, y, r]  )
                    color_img.itemset((y, x, 0)  ,       0  )
                    color_img.itemset((y, x, 1)  ,       0  )
                    color_img.itemset((y, x, 2)  ,       2_55  )
        return color_img, corner_list


if __name__ == "__main__":
 a       :						List[Any]       		=		HarrisCorner(0.04, 3)
 a		,			a       :						List[Any]       		=		edge_detect.detect('''path_to_image''')
 cva.imwrite('''detect.png''', color_img)